Any vehicle such as vessel has three attitude parameters, which are mostly defined as pitch, roll, and heading from true north. In hydrographic surveying, determination of these parameters by using GPS or INS technologies is essential for the requirements of vehicle measurements. Recently, integration of GPS/INS by using data fusion algorithm became more and more popular. Therefore, the data fusion algorithm plays an important role in vehicle attitude determination. To improve attitude determination accuracy and efficiency, two improved data fusion algorithms are presented, which are extended Kalman particle filter (EKPF) and genetic particle filter (GPF). EKPF algorithm combines particle filter (PF) with the extended Kalman filter (EKF) to avoid sample impoverishment during the resampling process. GPF is based on genetic algorithm and PF; several genetic operators such as selection, crossover, and mutation are adopted to optimize the resampling process of PF, which can not only reduce the particle impoverishment but also improve the computation efficiency. The performances of the system based on the two proposed algorithms are analyzed and compared with traditional KF. Simulation results show that, comprehensively considering the determination accuracy and consumption cost, the performance of the proposed GPF is better than EKPF and traditional KF.

It is very important to provide accurate and reliable attitude determination data since the performance of a vessel is highly reliant on the attitude determination system [

Block diagram of loosely-coupled GPS/INS system.

In the process of attitude determination, filtering method performs a very important role to achieve high accuracy determination results with high efficiency [

The major contributions of this paper are in investigating the EKPF and genetic particle filter (GPF) and using them to improve not only the accuracy of GPS/INS attitude determination but also the computation efficiency. The simulation results show that, compared with traditional KF, more highly accurate attitude determination results can be reached by using EKPF. The comparison results between EKPF and GPF show that GPF has higher filtering accuracy and more efficient computation ability than EKPF.

The state model for KF is presented as

The following are the measured state variables:

The measurement model is defined as

A set of vessel dynamic data are selected to verify the proposed filtering algorithms. The experiment parameters are as follows: gyro constant drifts of east, north, and up direction are all 1°/h; gyro random drift is 0.3°/h; accelerometer constant and random biases both are 0.08 mg; original heading, pitch, and roll angle are, respectively, 79.36°, 0°, and 0°; original velocity is 0.01 m/s and original velocity error is 0.01 m/s; and original longitude is 126.682234° and original latitude is 45.776563°. The GPS/INS system is shown in Figure

The GPS/INS system.

The INS data acquisition interface in PC.

The GPS data acquisition interface in PC.

The Kalman filter is a set of mathematical equations which can provide an efficient computational method to recursively estimate the state and error covariance of a process, in a way that minimizes the mean of the squared error covariance. The estimate process contains two steps: prediction and update. Consider a state space dynamic equation of a time-variant system model and a measurement model as

The equations for the KF are divided into two groups: time update equations and measurement update equations. The time update equations also can be thought of as predictor equations, while the measurement update equations can be thought of as corrector equations. If

PF algorithm is based on sequential importance sampling (SIS) step, which forms the basis for most sequential Monte Carlo filters. Compared with the traditional KF, PF is more suitable for nonlinear and non-Gaussian systems, so PF is gradually used in signal tracking, robot control, navigation and positioning, and many other fields. But it also has many drawbacks, such as degeneracy phenomenon, large amount of computation, and sample impoverishment caused by re-sampling. A more detailed description of PF is beyond the scope of this paper. The reader is encouraged to consult one of the many papers about the PF, such as [

In order to improve the performance of PF, EKF algorithm is introduced. It uses the local linearization method for approximation of the importance density moving the particles to the high likelihood region, and then the optimal importance density can be approximated. This filtering algorithm is called EKPF. The EKPF algorithm is summarized as follows.

Initialization:

Update the particle by EKF:

Particle importance weight after updating:

Normalize the importance weights:

State estimation:

Re-sampling:

The flow diagram of EKPF is shown as Figure

The flow diagram of EKPF.

Figures

Filtering results of heading angle by KF and EKPF.

Filtering results of pitch angle by KF and EKPF.

Filtering results of roll angle by KF and EKPF.

Comparisons of standard deviations.

Another evaluation criterion of algorithm performance is computation burden. In this paper, the calculation time of each output is used as evaluation indicator, which is shown in Table

Comparisons of consumption burden.

KF | EKPF | |
---|---|---|

Time ( |
423.20 | 1095.98 |

Genetic algorithms (GAs) are search methods based on the mechanization of natural selection and natural genetics. GAs combine survival of the fittest among string structures (chromosomes) with randomized information exchange. A simple GA consists of three stages: selection, crossover, and mutation. Selection is the process in which individual chromosomes are being selected according to their fitness function. By this process, the more likely chromosomes will contribute offspring in the next generation with higher probability. Crossover is the process that changing genetic information between two reproduced chromosomes occurs in. Even though the population can be improved by reproduction and crossover process, they can become overzealous and lose potentially important genetic information. Mutation process can protect against such an irrecoverable loss by simply altering a character with small probability every once in a while.

Aiming to solve the particle degeneracy phenomenon existing in the standard PF algorithm, GPF uses genetic algorithm as the re-sampling method of PF algorithm. The genetic selection, crossover, and mutation operations are introduced into GPF to improve the re-sampling process, which can not only reduce the particle degeneracy phenomenon but also decrease the computation time. The key point of GPF is using GA to improve the re-sampling process of PF; the diagram is shown in Figure

The flow diagram of GPF.

Here we only discuss the genetic algorithm scheme of re-sampling process. The details can be seen as follows.

Genetic Crossover Operation

Processing the selected particles by crossover algorithm, assume that the number of particles which need to be crossover is

Genetic Mutation Operation

The equation of mutation operation is

where,

After GA re-sampling, the state and variance can be estimated as

for from 1 to

for from 1 to

find particle

find particle

end

Re-calculate the weight of

end

Figures

Filtering results of heading angle by EKPF and GPF.

Filtering results of pitch angle by EKPF and GPF.

Filtering results of roll angle by EKPF and GPF.

Comparisons of standard deviations.

Table

Comparisons of consumption burden.

EKPF | GPF | |
---|---|---|

Time ( |
1095.98 | 786.53 |

The problem of choosing a suitable filter for attitude determination application is studied here. Due to the low filtering accuracy of KF and the particle degeneracy phenomenon of PF, two improved filters are presented in this paper, which are EKPF and GPF, respectively. And then the three filtering methods (KF, EKPF, and GPF) for attitude determination using GPS/INS system are studied, and their performances are compared.

The presented algorithms are tested with vessel attitude data, and the simulation results demonstrate that GPF yields the best accuracy under the same condition. In addition, the computation cost of the three filtering methods is analyzed in this paper; it shows that KF requires the lowest computation time, while EKPF requires the largest computation time. Comprehensively considering the filtering accuracy and computation cost, it can be concluded that the GPF is the most available filter among the three presented filtering methods.

This work is supported by Ocean special funds for scientific research on public causes (no. 201205035-09), Specialized Research Fund for the Doctoral Program of Higher Education (no. 20110092110039), National Natural Science Foundation of China (no. 50975049), 973 Program (no. 2009CB724002), Research Innovation Program for College Graduates of Jiangsu Province (no. CXZZ_0144), and The Scientific Research Foundation of Graduate School of Southeast University (no. ybjj1130).